The itemize items ball templates are defined in the beamerbaseauxtemplates.sty
:
% Itemize items, ball
\defbeamertemplate{itemize item}{ball}{\raise0.2pt\beamer@usesphere{item projected}{bigsphere}}
\defbeamertemplate{itemize subitem}{ball}{\raise0.2pt\beamer@usesphere{subitem projected}{smallsphere}}
\defbeamertemplate{itemize subsubitem}{ball}{\raise0.2pt\beamer@usesphere{subsubitem projected}{smallsphere}}
If you want to change the color for itemize and enumerate you can use
\setbeamercolor{item projected}{bg=red}
\setbeamercolor{subitem projected}{bg=green}
If you want to change only itemize (and not enumerate) then use
\setbeamercolor{itemize item}{bg=red}
\setbeamercolor{itemize subitem}{bg=green}
\makeatletter
\setbeamertemplate{itemize item}{\raise0.2pt\beamer@usesphere{itemize item}{bigsphere}}
\setbeamertemplate{itemize subitem}{\raise0.2pt\beamer@usesphere{itemize subitem}{smallsphere}}
\makeatother

Code:
\documentclass{beamer}
\usetheme{CambridgeUS}
\usecolortheme{spruce}
\usefonttheme{serif} % serif fonts for the entire beamer
\usepackage{amsmath}
\usepackage{enumerate} % To change the ennumerate style
\useoutertheme{tree}
\beamertemplatenavigationsymbolsempty %supressing navigation bar
\setbeamertemplate{subsection in toc}[subsections numbered]
\setbeamertemplate{section in toc}{\inserttocsectionnumber.~\inserttocsection}
% change the item and subitem color separatly (itemize and enumerate)
\setbeamercolor{item projected}{bg=red}
\setbeamercolor{subitem projected}{bg=green}
%%% change the item and subitem color separatly (only itemize)
%%\setbeamercolor{itemize item}{bg=red}
%%\setbeamercolor{itemize subitem}{bg=green}
%%\makeatletter
%%\setbeamertemplate{itemize item}{\raise0.2pt\beamer@usesphere{itemize item}{bigsphere}}
%%\setbeamertemplate{itemize subitem}{\raise0.2pt\beamer@usesphere{itemize subitem}{smallsphere}}
%%\makeatother
\begin{document}
\begin{frame}{Probability}
\begin{itemize}
\item \textbf{Probability} expresses a degree of belief a person has about an event or a statement by a number between zero and one.
\item \textbf{Two Schools of Statistical Inference:}
\begin{itemize}
\item \textit{Bayesian Inference} - common usage.
\item \textit{Classical Inference} - The classical statistician uses the word probability only for an event which can be repeated, and interprets it as the limit of the empirical frequency of the event as the number of repititions increases indefinitely.
\end{itemize}
\item The two methods are complimentary and diferent situations call for different methods.
\end{itemize}
\end{frame}
\end{document}
\setbeamercolor{itemize item}{fg=red} \setbeamercolor{itemize subitem}{fg=blue}